Andrej Bauer wrote:
> For example Pour-El and Richards have an example of a wave equation
> whose initial condition (time t=0) is computable but the solution is not
> computable at time t=1.
In 1983 John Baez showed that this negative result necessarily depends
on the physics being classical, by showing that both the n-particle
Coulombic Hamiltonian itself and the time evolution of n-particle
systems governed by it are recursive, see Baez, J.C., Recursivity in
quantum mechanics, Trans. Am. Math. Soc., 280:1, 339-350 (Nov. 1983),
online at http://math.ucr.edu/home/baez/recursivity.pdf or (higher
resolution) at http://www.jstor.org/stable/1999617.pdf
Vaughan Pratt